Correlation of parametric and nonparametric statistics for applications in signal detection

In this paper, we address correlation coefficients among some representative statistics of independent and identically distributed random signals. The lower and upper bounds on the correlation coefficients are obtained for random signals and their ranks, magnitudes, and magnitude ranks, which in general may or may not be correlated. Examples of specific distributions are given for the bounds, and implications of the correlation coefficients in signal detection applications are indicated.